I think there's a close correspondence though. What you naively think of as a knot is a mathematical knot if you join the ends together, and I think any given m

I think there's a close correspondence though. What you naively think of as a knot is a mathematical knot if you join the ends together, and I think any given mathematical knot can give rise to a regular knot. I know very little about it other than a friend of mine did a PhD in it, but it gets weird fast. Like they often consider it in canonical forms that look nothing like a practice knot, and then of course they start showing correspondences with polynomials &c.